Boat Word Problem

The name of the pictureThe name of the pictureThe name of the pictureClash Royale CLAN TAG#URR8PPP











up vote
0
down vote

favorite













A crew can row a certain course upstream in 84 minutes;
they can row the same course down stream in 9 minutes less than
they can row it in still water: how long would they take to row
down with the stream.




The equations I came up with are:



$$fracdx - y = 84$$
$$fracdx + y = fracdx - 9$$



Where $d$ is the distance covered in their course, $x$ is the rate of the people rowing the boat, and $y$ is the rate of the stream.



I tried substituting $d$ with $84(x -y)$, and that rendered the equation $3x^2 - 25xy + 28y^2 = 0$. As far as I know, this equation isn't solvable. Any attempts I make to obtain other equations or results leads to this same equation.



If there's any alternate method to solving this, I would love to know.



Thanks.




word-problem




share|cite|improve this question

























    up vote
    0
    down vote

    favorite













    A crew can row a certain course upstream in 84 minutes;
    they can row the same course down stream in 9 minutes less than
    they can row it in still water: how long would they take to row
    down with the stream.




    The equations I came up with are:



    $$fracdx - y = 84$$
    $$fracdx + y = fracdx - 9$$



    Where $d$ is the distance covered in their course, $x$ is the rate of the people rowing the boat, and $y$ is the rate of the stream.



    I tried substituting $d$ with $84(x -y)$, and that rendered the equation $3x^2 - 25xy + 28y^2 = 0$. As far as I know, this equation isn't solvable. Any attempts I make to obtain other equations or results leads to this same equation.



    If there's any alternate method to solving this, I would love to know.



    Thanks.




    word-problem




    share|cite|improve this question























      up vote
      0
      down vote

      favorite









      up vote
      0
      down vote

      favorite












      A crew can row a certain course upstream in 84 minutes;
      they can row the same course down stream in 9 minutes less than
      they can row it in still water: how long would they take to row
      down with the stream.




      The equations I came up with are:



      $$fracdx - y = 84$$
      $$fracdx + y = fracdx - 9$$



      Where $d$ is the distance covered in their course, $x$ is the rate of the people rowing the boat, and $y$ is the rate of the stream.



      I tried substituting $d$ with $84(x -y)$, and that rendered the equation $3x^2 - 25xy + 28y^2 = 0$. As far as I know, this equation isn't solvable. Any attempts I make to obtain other equations or results leads to this same equation.



      If there's any alternate method to solving this, I would love to know.



      Thanks.




      word-problem




      share|cite|improve this question














      A crew can row a certain course upstream in 84 minutes;
      they can row the same course down stream in 9 minutes less than
      they can row it in still water: how long would they take to row
      down with the stream.




      The equations I came up with are:



      $$fracdx - y = 84$$
      $$fracdx + y = fracdx - 9$$



      Where $d$ is the distance covered in their course, $x$ is the rate of the people rowing the boat, and $y$ is the rate of the stream.



      I tried substituting $d$ with $84(x -y)$, and that rendered the equation $3x^2 - 25xy + 28y^2 = 0$. As far as I know, this equation isn't solvable. Any attempts I make to obtain other equations or results leads to this same equation.



      If there's any alternate method to solving this, I would love to know.



      Thanks.





      word-problem





      share|cite|improve this question












      share|cite|improve this question




      share|cite|improve this question








      edited 7 hours ago
























      asked 7 hours ago









      A Silent Cat

      1227




      1227




















          2 Answers
          2






          active

          oldest

          votes

















          up vote
          1
          down vote



          accepted










          That equation is perfectly solvable. You're implicitly assuming $x$ and $y$ are non-negative from the way you've structured your equations, so you can fix a non-negative $y$ and try and figure out if there exists a positive solution $x$. That is, if we fix $y$, then



          $$3x^2-75yx+28y^2=0$$



          is a regular old quadratic equation in $x$. The solution will be some formula involving $y$, and you can check for which $y$ that formula gives a positive real number.






          share|cite|improve this answer





















          • Can't believe I didn't realize that...Thanks.
            – A Silent Cat
            7 hours ago

















          up vote
          0
          down vote













          HINT



          Your task is not to figure out $d,x,$ or $y$, your task is to figure out how long it takes the crew to go down with the stream.






          share|cite|improve this answer





















            Your Answer




            StackExchange.ifUsing("editor", function ()
            return StackExchange.using("mathjaxEditing", function ()
            StackExchange.MarkdownEditor.creationCallbacks.add(function (editor, postfix)
            StackExchange.mathjaxEditing.prepareWmdForMathJax(editor, postfix, [["$", "$"], ["\\(","\\)"]]);
            );
            );
            , "mathjax-editing");

            StackExchange.ready(function()
            var channelOptions =
            tags: "".split(" "),
            id: "69"
            ;
            initTagRenderer("".split(" "), "".split(" "), channelOptions);

            StackExchange.using("externalEditor", function()
            // Have to fire editor after snippets, if snippets enabled
            if (StackExchange.settings.snippets.snippetsEnabled)
            StackExchange.using("snippets", function()
            createEditor();
            );

            else
            createEditor();

            );

            function createEditor()
            StackExchange.prepareEditor(
            heartbeatType: 'answer',
            convertImagesToLinks: true,
            noModals: false,
            showLowRepImageUploadWarning: true,
            reputationToPostImages: 10,
            bindNavPrevention: true,
            postfix: "",
            noCode: true, onDemand: true,
            discardSelector: ".discard-answer"
            ,immediatelyShowMarkdownHelp:true
            );



            );








             

            draft saved


            draft discarded


















            StackExchange.ready(
            function ()
            StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f2873196%2fboat-word-problem%23new-answer', 'question_page');

            );

            Post as a guest

















            2 Answers
            2






            active

            oldest

            votes








            2 Answers
            2






            active

            oldest

            votes









            active

            oldest

            votes






            active

            oldest

            votes








            up vote
            1
            down vote



            accepted










            That equation is perfectly solvable. You're implicitly assuming $x$ and $y$ are non-negative from the way you've structured your equations, so you can fix a non-negative $y$ and try and figure out if there exists a positive solution $x$. That is, if we fix $y$, then



            $$3x^2-75yx+28y^2=0$$



            is a regular old quadratic equation in $x$. The solution will be some formula involving $y$, and you can check for which $y$ that formula gives a positive real number.






            share|cite|improve this answer





















            • Can't believe I didn't realize that...Thanks.
              – A Silent Cat
              7 hours ago














            up vote
            1
            down vote



            accepted










            That equation is perfectly solvable. You're implicitly assuming $x$ and $y$ are non-negative from the way you've structured your equations, so you can fix a non-negative $y$ and try and figure out if there exists a positive solution $x$. That is, if we fix $y$, then



            $$3x^2-75yx+28y^2=0$$



            is a regular old quadratic equation in $x$. The solution will be some formula involving $y$, and you can check for which $y$ that formula gives a positive real number.






            share|cite|improve this answer





















            • Can't believe I didn't realize that...Thanks.
              – A Silent Cat
              7 hours ago












            up vote
            1
            down vote



            accepted







            up vote
            1
            down vote



            accepted






            That equation is perfectly solvable. You're implicitly assuming $x$ and $y$ are non-negative from the way you've structured your equations, so you can fix a non-negative $y$ and try and figure out if there exists a positive solution $x$. That is, if we fix $y$, then



            $$3x^2-75yx+28y^2=0$$



            is a regular old quadratic equation in $x$. The solution will be some formula involving $y$, and you can check for which $y$ that formula gives a positive real number.






            share|cite|improve this answer













            That equation is perfectly solvable. You're implicitly assuming $x$ and $y$ are non-negative from the way you've structured your equations, so you can fix a non-negative $y$ and try and figure out if there exists a positive solution $x$. That is, if we fix $y$, then



            $$3x^2-75yx+28y^2=0$$



            is a regular old quadratic equation in $x$. The solution will be some formula involving $y$, and you can check for which $y$ that formula gives a positive real number.







            share|cite|improve this answer













            share|cite|improve this answer



            share|cite|improve this answer











            answered 7 hours ago









            Jack M

            16.9k33473




            16.9k33473











            • Can't believe I didn't realize that...Thanks.
              – A Silent Cat
              7 hours ago
















            • Can't believe I didn't realize that...Thanks.
              – A Silent Cat
              7 hours ago















            Can't believe I didn't realize that...Thanks.
            – A Silent Cat
            7 hours ago




            Can't believe I didn't realize that...Thanks.
            – A Silent Cat
            7 hours ago










            up vote
            0
            down vote













            HINT



            Your task is not to figure out $d,x,$ or $y$, your task is to figure out how long it takes the crew to go down with the stream.






            share|cite|improve this answer

























              up vote
              0
              down vote













              HINT



              Your task is not to figure out $d,x,$ or $y$, your task is to figure out how long it takes the crew to go down with the stream.






              share|cite|improve this answer























                up vote
                0
                down vote










                up vote
                0
                down vote









                HINT



                Your task is not to figure out $d,x,$ or $y$, your task is to figure out how long it takes the crew to go down with the stream.






                share|cite|improve this answer













                HINT



                Your task is not to figure out $d,x,$ or $y$, your task is to figure out how long it takes the crew to go down with the stream.







                share|cite|improve this answer













                share|cite|improve this answer



                share|cite|improve this answer











                answered 7 hours ago









                Bram28

                54.5k33776




                54.5k33776






















                     

                    draft saved


                    draft discarded


























                     


                    draft saved


                    draft discarded














                    StackExchange.ready(
                    function ()
                    StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f2873196%2fboat-word-problem%23new-answer', 'question_page');

                    );

                    Post as a guest
































































                    Comments

                    Post a Comment

                    Popular posts from this blog

                    What is the equation of a 3D cone with generalised tilt?

                    Image
                    Clash Royale CLAN TAG #URR8PPP up vote 2 down vote favorite What is the equation of a 3D cone with generalized tilt? I've noticed that in most equations given to represent a cone, there is no parameter which defines the tilt of the cone in 3D space and that most of them have their point at the origin $(0,0,0)$ - I was wondering if anyone could give me a more generalized cone equation for a cone in any position in 3D space 3d share | cite | improve this question edited Jul 25 '16 at 0:05 ervx 9,425 3 13 36 asked Jul 24 '16 at 15:38 Charlene 11 2 2 Welcome to Math.SE! Could you please explain a few things to help people give an answer useful to you: 1. What do you mean by "generalized tilt"? 2. Are you asking about a right circular cone? Does the angle at the vertex matter? 3. What form of answer (implicit, parametric...?) are you looking for? 4. If this is homework, what tools do you have available, an...
                    Read more

                    Color the edges and diagonals of a regular polygon

                    Image
                    Clash Royale CLAN TAG #URR8PPP up vote 5 down vote favorite 1 Here is the problem: For what $n$ is it possible to color the edges and diagonals of an $n$-side regular polygon with $dfracbinomn23$ colors, such that you use every color exactly three times and for every color the three segments (edges or diagonals) with that color form a triangle? Trivially $nequiv 0 text or 1 pmod3$. I can also prove that if the statement is true for $k$ than it is true for $3k$ as well. How to finish? Please help! Thanks combinatorial-geometry share | cite | improve this question edited Aug 6 at 21:57 alcana 118 4 asked Aug 6 at 21:15 Leo Gardner 356 11 Even assuming "polyhpn" in the title is a typo for polygon , it is unclear what you mean by "the edges and sides". Aren't the side of a regular polygon the same as the edges? A regular $n$-sided polygon has $n$ edges. – hardmath Aug 6 at 21:20 3 $n$ ne...
                    Read more

                    Relationship between determinant of matrix and determinant of adjoint?

                    Image
                    Clash Royale CLAN TAG #URR8PPP up vote 2 down vote favorite We are studying adjoints in class, and I was curious if there is a relationship between the determinant of matrix A, and the determinant of the adjoint of matrix A? I assume there would be a relationship because finding the adjoint requires creating a cofactor matrix and then transposing it. linear-algebra determinant adjoint-operators share | cite | improve this question asked Nov 17 '17 at 17:32 CluelessCoder 32 5 For a square matrix $A$ of order $n$, we have $A(operatornameadj A)=(operatornameadj A)A=|A|I_n$ where $I_n$ is the identity matrix of order $n$. This should tell you about the determinant of the adjoint in terms of that of $A$ (use multiplicative property and other elementary properties of determinants). – Prasun Biswas Nov 17 '17 at 17:35 1 @CluelessCoder: see here: math.stackexchange.com/questions/516127/…...
                    Read more